The section of canon law on marriage starts
here. Canon 1066 requires priests to ensure that all necessary annulments have been obtained. The complementary norms applicable in the U.S. can be found
here. Canon 1085 defines the diriment impediment of prior bond (ligamen). In particular:
Can. 1085 §2. Even if the prior marriage is invalid or dissolved for any reason, it is not on that account permitted to contract another before the nullity or dissolution of the prior marriage is established legitimately and certainly.
The instruction on handling annulments is
here. Article 145 requires that a person who needs multiple annulments must have them done in chronological order.
Thanks.